﻿ 高速舰船的运动模型适用性分析及海浪中的操纵仿真试验
 舰船科学技术  2018, Vol. 40 Issue (1): 41-45 PDF

1. 海军工程大学 电气工程学院，湖北 武汉 430033;
2. 海军九〇二厂，上海 200083

The applicability analysis of the model of high-speed ship and the simulated maneuvering test in waves
SUN Jian1, CHEN Yong-bing1, ZHOU Gang1, XU Wu-nong2
1. Electrical Engineering College, Naval University of Engineering, Wuhan 430033, China;
2. Navy 902 Factory, Shanghai 200083, China
Abstract: Building the ship model has important significance for the study of ship motion control algorithms and research of autopilot. The three-degree of freedom model is simple and applicative to the low-speed or medium-speed ship. But the maneuverability of high-speed ship is different. There may be large amplitude rolling during the turning motion and the effect of coupling of rolling and yawing is obvious. A four-degree of freedom model of combatant DTMB5415 was established and validated by the comparison of pool test and the simulated maneuvering test. Then this model was applied to discuss the influence of the wave interference forces to the high-speed ship.
Key words: ship model     coupling of roll     wave interference force
0 引 言

1 静水中的船舶运动模型

 $\left\{ {\begin{array}{*{20}{l}}{(m + {m_x})\dot u - (m + {m_y})vr = {X_H} + {X_P} + {X_R} + {X_W}}\text{，}\\{(m + {m_y})\dot v + (m + {m_x})ur = {Y_H} + {Y_R} + {Y_W}}\text{，}\\{({I_{ZZ}} + {J_{ZZ}})\dot r = {N_H} + {N_R} + {N_W}}\text{。}\end{array}} \right.$ (1)

 $\left\{ {\begin{array}{*{20}{l}}{{Y_H} = {Y_0}(v,r) + {Y_1}(v,r,\phi )}\text{，}\\{{N_H} = {N_0}(v,r) + {N_1}(v,r,\phi ) - {Y_H} \cdot {x_C}}\text{。}\end{array}} \right.$ (2)

 $\left\{ {\begin{array}{*{20}{l}}{{Y_1}(v,r,\phi ) = 0}\text{，}\\{{N_1}(v,r,\phi ) = {N_\phi }\phi + {N_{v\phi }}v\left| \phi \right| + {N_{r\phi }}r\left| \phi \right|}\text{。}\end{array}} \right.$ (3)

 $({I_{xx}} + {J_{xx}})\ddot \phi = {L_H} + {L_R} + {L_W}\text{。}$ (4)

 ${L_H} = - N(\dot \phi ) - W \cdot GZ(\phi ) - {Y_H} \cdot {z_H}\text{。}$ (5)

2 海浪干扰模型的建立

2.1 不规则波的数学描述

 $\zeta (t) = \sum\limits_{i = 1}^m {\sqrt {2{S_\zeta }({\omega _i})\Delta \omega } } \cos (\frac{{{\omega _i}^2}}{g}\xi - {\omega _i}t + {\varepsilon _i})\text{。}$ (6)

 ${S_\xi }(\omega ) = \frac{A}{{{\omega ^5}}}\exp ( - \frac{B}{{{\omega ^4}}})\text{。}$ (7)

 图 1 海浪波谱密度曲线 Fig. 1 The spectrum curve of wave
2.2 波浪干扰力的计算

 ${L_{wave}}(t) = \sum\limits_{i = 1}^n {{L_{wave}}({\omega _i}) \cdot \zeta (t)}\text{。}$ (8)

2.3 波浪漂移力及力矩的计算

 $\left\{ {\begin{array}{*{20}{c}}{X_{wave}^D = \frac{1}{2}\rho L\cos \chi \sum\limits_{i = 1}^m {C_{Xw}^D({\lambda _i}){a_i}^2} }\text{，}\\{Y_{wave}^D = \frac{1}{2}\rho L\sin \chi \sum\limits_{i = 1}^m {C_{Yw}^D({\lambda _i}){a_i}^2} }\text{，}\\{N_{wave}^D = \frac{1}{2}\rho {L^2}\sin \chi \sum\limits_{i = 1}^m {C_{Nw}^D({\lambda _i}){a_i}^2} }\text{。}\end{array}} \right.$ (9)

3 操纵仿真试验

 图 2 仿真原理框图 Fig. 2 The block diagram of simulation
3.1 不同舵角下的船舶回转运动仿真

 图 3 35°舵角下DTMB5415船的回转运动仿真图 Fig. 3 The simulation diagram of DTMB5415 under the rudder angle of 35°

 图 4 25°舵角下DTMB5415船的回转运动仿真图 Fig. 4 The simulation diagram of DTMB5415 under the rudder angle of 25°

3.2 波浪干扰下的船舶回转运动仿真

 图 5 波浪干扰下DTMB5415船的横摇角变化曲线 Fig. 5 The curve of rolling angle of ship DTMB5415 under the wave interference

 图 6 波浪干扰下DTMB5415船回转运动仿真图 Fig. 6 The simulation diagram of ship DTMB5415 under the wave interference

4 结 语

本文通过Matlab对DTMB5415船分别进行了三自由度运动建模以及加入横摇的四自由度运动建模，通过仿真操纵实验得到了回转运动过程中的纵向速度、首摇角、横摇角等运动状态量，分析了回转运动中横摇角的变化规律，可以看出对于高速舰船，大舵角回转时的稳定横摇角可以达到5°以上。另一方面，横摇运动耦合作用增大了绕Z轴的回转力矩。通过将不同舵角下加横摇、不加横摇2次仿真的回转圈的特征参数与水池试验结果进行对比及误差分析，可以看出：由于回转过程中较大的横摇角，三自由度运动方程已不能够满足实用的要求，加横摇运动模型相对于水池试验结果的误差比不加横摇的三自由度运动模型大大降低。

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